Question

In this activity, you will experiment with rolling a six-sided die a number of times and find the average of the results. You will see how varying the sample size in terms of the number of times the die is rolled causes a variation in the results obtained. Open the dice roller and follow the instructions below to complete the activity.

Follow these steps to complete the first roll:

Select 1 for Number of dice, and click Session as the Results option.
Type the number 10 in the Auto Roll box, and click the Auto Roll button once. This simulates rolling the die 10 times.
In the Session column of the Results table, you will now see percentages and fractions in parentheses. Pay attention to the numerator of the fraction. This value tells you how many times out of 10 rolls each of the six numbers (1 through 6) was rolled.
If you make an error and would like to start over, click the Back button. Then select Play under Dice Roll. Repeat steps 1 through 3.
Part A
What is the average of the first 10 rolls of the die? Enter your results in the table. (Hint: To find the average of 10 rolls, multiply each number rolled by the number of times it was rolled. Then add the products, and divide the sum by 10.)

Answer 1

To find the average of the first 10 rolls of the die, we need to multiply each number rolled by the number of times it was rolled, then add the products and divide by the total number of rolls (which is 10 in this case).

Let's use the results table to record the number of times each number (1 through 6) was rolled in the first 10 rolls:

| Number | Number of times rolled |
| ------ | --------------------- |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |

Based on the instructions, we know that we need to look at the numerator of the fraction in the Session column of the Results table to find the number of times each number was rolled. Let's fill in the table:

| Number | Number of times rolled |
| ------ | --------------------- |
| 1 | 1 |
| 2 | 2 |
| 3 | 2 |
| 4 | 1 |
| 5 | 2 |
| 6 | 2 |

To find the average, we multiply each number rolled by the number of times it was rolled, add the products, and divide by the total number of rolls:

Average = (1 x 1 + 2 x 2 + 3 x 2 + 4 x 1 + 5 x 2 + 6 x 2) / 10
Average = 3.7

Therefore, the average of the first 10 rolls of the die is 3.7.